AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

Consider the expression,

√‌

x

2x+1

+√‌

2x+1

x

=2‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I)

Let,

√‌

x

2x+1

=y

then y+‌

1

y

‌‌=2

y2−2y+1‌‌=0

(y−1)(y−1)‌‌=0

(y−1)2‌‌=0
Simplify further
y−1‌‌=0
y‌‌=1

√‌

x

2x+1

‌‌=1
‌

x

2x+1

‌‌=1
Solve further

2x+1‌‌=x
x‌‌=−1

Here, α satisfies equation (I),so,α=−1, now

α2x2+4αx+3‌‌=0
(−1)2x2+4(−1)x+3‌‌=0
x2−4x+3‌‌=0
x‌‌=1,3